Safe Haskell	Safe
Language	Haskell2010

Fcf.Class.Monoid

Contents

Pure type families
First-class families

Description

Semigroups and monoids.

Synopsis

type family (x :: a) <> (y :: a) :: a
type family MEmpty :: a
data (.<>) :: a -> a -> Exp a
data MEmpty_ :: Exp a

Pure type families

Nicer to use when applied explicitly.

type family (x :: a) <> (y :: a) :: a Source #

Type-level semigroup composition (<>).

Instances

type LT <> (_b :: Ordering) Source #
Instance details Defined in Fcf.Class.Monoid type LT <> (_b :: Ordering) = LT
type EQ <> (b :: Ordering) Source #
Instance details Defined in Fcf.Class.Monoid type EQ <> (b :: Ordering) = b
type GT <> (_b :: Ordering) Source #
Instance details Defined in Fcf.Class.Monoid type GT <> (_b :: Ordering) = GT
type (a :: Ordering) <> EQ Source #
Instance details Defined in Fcf.Class.Monoid type (a :: Ordering) <> EQ = a
type (_a :: ()) <> (_b :: ()) Source #
Instance details Defined in Fcf.Class.Monoid type (_a :: ()) <> (_b :: ()) = ()
type (All a :: All) <> (All b :: All) Source #
Instance details Defined in Fcf.Class.Monoid type (All a :: All) <> (All b :: All) = All (a && b)
type (Any a :: Any) <> (Any b :: Any) Source #
Instance details Defined in Fcf.Class.Monoid type (Any a :: Any) <> (Any b :: Any) = Any (a \|\| b)
type (a2 :: Maybe a1) <> (Nothing :: Maybe a1) Source #
Instance details Defined in Fcf.Class.Monoid type (a2 :: Maybe a1) <> (Nothing :: Maybe a1) = a2
type ([] :: [k]) <> (ys :: [k]) Source #
Instance details Defined in Fcf.Class.Monoid type ([] :: [k]) <> (ys :: [k]) = ys
type (Nothing :: Maybe a) <> (b :: Maybe a) Source #
Instance details Defined in Fcf.Class.Monoid type (Nothing :: Maybe a) <> (b :: Maybe a) = b
type (Just a2 :: Maybe a1) <> (Just b :: Maybe a1) Source #
Instance details Defined in Fcf.Class.Monoid type (Just a2 :: Maybe a1) <> (Just b :: Maybe a1) = Just (a2 <> b)
type (Endo f :: Endo a) <> (Endo g :: Endo a) Source #
Instance details Defined in Fcf.Class.Monoid.Types type (Endo f :: Endo a) <> (Endo g :: Endo a) = Endo (f <=< g)
type (x ': xs :: [a]) <> (ys :: [a]) Source #
Instance details Defined in Fcf.Class.Monoid type (x ': xs :: [a]) <> (ys :: [a]) = x ': (xs <> ys)
type ((,) a1 a2 :: (k2, k1)) <> ((,) b1 b2 :: (k2, k1)) Source #
Instance details Defined in Fcf.Class.Monoid type ((,) a1 a2 :: (k2, k1)) <> ((,) b1 b2 :: (k2, k1)) = (,) (a1 <> b1) (a2 <> b2)
type ((,,) a1 a2 a3 :: (k2, k1, k3)) <> ((,,) b1 b2 b3 :: (k2, k1, k3)) Source #
Instance details Defined in Fcf.Class.Monoid type ((,,) a1 a2 a3 :: (k2, k1, k3)) <> ((,,) b1 b2 b3 :: (k2, k1, k3)) = (,,) (a1 <> b1) (a2 <> b2) (a3 <> b3)

type family MEmpty :: a Source #

Type-level monoid identity mempty.

Examples

Expand

>>> :kind! 'LT <> MEmpty
'LT <> MEmpty :: Ordering
= 'LT

>>> :kind! MEmpty <> '( 'EQ, '[1, 2])
MEmpty <> '( 'EQ, '[1, 2]) :: (Ordering, [Nat])
= '( 'EQ, '[1, 2])

>>> :kind! '( 'GT, 'Just '()) <> MEmpty
'( 'GT, 'Just '()) <> MEmpty :: (Ordering, Maybe ())
= '( 'GT, 'Just '())

Instances

type MEmpty Source #
Instance details Defined in Fcf.Class.Monoid type MEmpty = EQ
type MEmpty Source #
Instance details Defined in Fcf.Class.Monoid type MEmpty = ()
type MEmpty Source #
Instance details Defined in Fcf.Class.Monoid type MEmpty = All True
type MEmpty Source #
Instance details Defined in Fcf.Class.Monoid type MEmpty = Any False
type MEmpty Source #
Instance details Defined in Fcf.Class.Monoid type MEmpty = ([] :: [k])
type MEmpty Source #
Instance details Defined in Fcf.Class.Monoid type MEmpty = (Nothing :: Maybe a)
type MEmpty Source #
Instance details Defined in Fcf.Class.Monoid.Types type MEmpty = Endo (Pure :: a -> a -> Type)
type MEmpty Source #
Instance details Defined in Fcf.Class.Monoid type MEmpty = (,) (MEmpty :: k1) (MEmpty :: k2)
type MEmpty Source #
Instance details Defined in Fcf.Class.Monoid type MEmpty = (,,) (MEmpty :: k1) (MEmpty :: k2) (MEmpty :: k3)

First-class families

Can be composed and passed to higher-order functions.

data (.<>) :: a -> a -> Exp a Source #

Type-level semigroup composition (<>).

This is the fcf-encoding of (<>). To define a new semigroup, add type instances to (<>).

Instances

type Eval (x .<> y :: a -> Type) Source #
Instance details Defined in Fcf.Class.Monoid type Eval (x .<> y :: a -> Type) = x <> y

data MEmpty_ :: Exp a Source #

Type-level monoid identity mempty.

This is the fcf-encoding of MEmpty.

Instances

type Eval (MEmpty_ :: a -> Type) Source #
Instance details Defined in Fcf.Class.Monoid type Eval (MEmpty_ :: a -> Type) = (MEmpty :: a)